Deceitfully tells you how someone did a thing: in a lying, tricky way, so that other people would believe what is not true. It goes with a verb, not with a person-noun. She deceitfully hid the letter means she hid it in order to mislead; he answered deceitfully means the answer was shaped to fool someone. It is the adverb partner of deceitful, and it keeps the same moral weight — this is not a cute trick, it is dishonest on purpose.